Vyxal 3, 7 bytes
ė*∦⌊⌈$*
Takes two integers as its argument and returns two integers. Works the same as various other answers including @mathscat’s Vyxal one and @UnrelatedString’s Jelly one.
Explanation
ė*∦⌊⌈$*
ė | ReciprocslReciprocal of n
* | To the power of p
∦⌊⌈ | Pair ceiling with floor and wrap in a list
$* | To the power of p
```